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Points \(P\), \(Q\), \(R\) and \(S\) divide the respective sides of rectangle \(ABCD\) in the proportion \(1:2\). If the area of rectangle \(ABCD\) is \(1\), find the area quadrilateral \(PQRS\).

 

 Jan 9, 2021
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[  ABCD   ] =    width * height  = 1    =  wh

 

Area  of  right  triangle DRS   =  area of right triangle PBQ  =  (1/2) (2/3)w* (1/3) h =  ( 1/9)wh

 

Area of  right  triangle RCQ  = area of triangle  SAP   = (1/2) ( 1/3) h ( (2/3)w =  ( 1/9)wh

 

So   these  combined areas =  4 ( 1/9) wh  =   (4/9) wh  = (4/9) (1)   =4/9

 

[ PQRS ]  =  [ ABCD ] - 4/9  =     1  -  4/9   =  5/9  

 

 

cool cool cool

 Jan 9, 2021

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